This paper focuses on studying the Noether-Mei symmetry and the conserved quantity for dynamical systems with non-standard Lagrangians (exponential Lagrangians and power law Lagrangians). Firstly, The definition and the criteria of Noether-Mei symmetry for dynamical systems with non-standard Lagrangians are given. Secondly, The conditions that Noether-Mei symmetry leads to Noether conserved quantity or Mei conserved quantity and the form of conserved quantities are put forward. And four theorems for Noether-Mei symmetry and conserved quantities are established. Two examples are given to illustrate the application of the results.